Someone at a philosophy club asked me about the Higgs boson, and I was saying the usual stuff about how it's the Higgs field which does the real work, and 'the Higgs boson' is actually just a leftover, the only one of four Higgs field excitations which doesn't even get absorbed into a gauge boson... but the Higgs mass does turn out to be important and mysterious since it indicates our vacuum is critically tuned by unknown means and for unknown reasons. Oh, and there's also a theory that the Higgs is the inflaton.
Afterwards I was thinking, isn't it strange that the leftover Higgs boson should happen to be the messenger of criticality? Is there some theoretical framework, in which this neat division of labor between seemingly disparate tasks - electroweak goldstones, and messenger of criticality - makes sense, is to be expected, is the product of a deeper unity? That's the question for today.
Some intuition makes me think of conformal symmetry breaking. As if the Higgs is a top condensate that spontaneously breaks conformal symmetry and electroweak symmetry at the same time, and the mechanics of the process is responsible for giving it a critically tuned mass. But I do not know a mechanism that works this way.
